You have $4$ reindeer, Bloopin, Balthazar, Gloopin, and Prancer, and you want to have $3$ fly your sleigh. You always have your reindeer fly in a single-file line. How many different ways can you arrange your reindeer?
Solution: We can build our line of reindeer one by one: there are $3$ slots, and we have $4$ different reindeer we can put in the first slot. Once we fill the first slot, we only have $3$ reindeer left, so we only have $3$ choices for the second slot. So far, there are $4 \cdot 3 = 12$ unique choices we can make. We can continue in this way for the third reindeer, where we will have $2$ choices. So, the total number of unique choices we could make to get to an arrangement of reindeer is $4\cdot3\cdot2$. Another way of writing this is $\dfrac{4!}{(4-3)!} = 24$